I know a few friends who lives/lived in Jersey and took long commute to Manhattan. They are not "living in the city" by any shot; their relationship ends at 7-8PM when their shift ends and they have to take their long commute back.

Manhattan is attractive because it's much easier (at least pre-2019) to get a job there when you have little skills (a bartender can actually be a skilled job and requires certain connections) and need cash fast. There is also a community of people in the same situation (especially if you are a new immigrant).

Perhaps, but there's also plenty of NYC bartenders who don't particularly want to be bartenders, it's just a job they managed to get and it's what they're doing to pay the bills.